CAREER: Investigating Differentiated Instruction and Relationships between Rational Number Knowledge and Algebraic Reasoning in Middle School
职业:调查中学有理数知识与代数推理的差异化教学及关系
基本信息
- 批准号:1252575
- 负责人:
- 金额:$ 64.65万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2013
- 资助国家:美国
- 起止时间:2013-08-01 至 2020-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Middle school mathematics classrooms are marked by increasing cognitive diversity and students' persistent difficulties in learning algebra. Currently middle school mathematics instruction in a single classroom is often not differentiated for different thinkers, which can bore some students or overly challenge others. One way schools often deal with different thinkers at the same grade level is by tracking, which has also been shown to have deleterious effects on students, both cognitively and affectively. In addition, students continue to struggle to learn algebra, and increasing numbers of middle school students are receiving algebra instruction. The proposed project initiates new research and an integrated education plan to address these problems by investigating (1) how to effectively differentiate instruction for middle school students at different reasoning levels; and (2) how to foster middle school students' algebraic reasoning and rational number knowledge in mutually supportive ways. Educational goals of the project are to enhance the abilities of prospective and practicing teachers to teach cognitively diverse students, to improve doctoral students' understanding of relationships between students' learning and teachers' practice, and to form a community of mathematics teachers committed to on-going professional learning about how to differentiate instruction.Three research-based products are being developed: two learning trajectories, materials for differentiating instruction developed collaboratively with teachers, and a written assessment to evaluate students' levels of reasoning. The first trajectory, elaborated for students at each of three levels of reasoning, focuses on developing algebraic expressions and solving basic equations that involve rational numbers; the second learning trajectory, also elaborated for students at each of three levels of reasoning, focuses on co-variational reasoning in linear contexts. In addition, the project investigates how students' classroom experience is influenced by differentiated instruction, which will allow for comparisons with research findings on student experiences in tracked classrooms. Above all, the project enhances middle school mathematics teachers' abilities to serve cognitively diverse students. This aspect of the project has the potential to decrease opportunity gaps. Finally, the project generates an understanding of the kinds of support needed to help prospective and practicing teachers learn to differentiate instruction.The project advances discovery and understanding while promoting teaching, training, and learning by (a) integrating research into the teaching of middle school mathematics, (b) fostering the learning of all students by tailoring instruction to their cognitive needs, (c) partnering with practicing teachers to learn how to implement this kind of instruction, (d) improving the training of prospective mathematics teachers and graduate students in mathematics education, and (e) generating a community of mathematics teachers who engage in on-going learning to differentiate instruction. The project broadens participation by including students from underrepresented groups, particularly those with learning disabilities. Results from the project will be broadly disseminated via conference presentations; articles in diverse media outlets; and a project website that will make project products available, be a location for information about the project for the press and the public, and be a tool to foster teacher-to-teacher communication.
中学数学课堂的特点是认知多样性不断增加,而学生在学习代数方面持续存在困难。目前,在一个教室里进行的中学数学教学往往没有针对不同的思考者进行区分,这可能会让一些学生感到厌烦或过度挑战其他学生。学校经常与同一年级的不同思想家打交道的一种方法是跟踪,这也被证明对学生的认知和情感都有有害影响。此外,学生们继续努力学习代数,越来越多的中学生正在接受代数教学。拟议的项目启动了新的研究和综合教育计划来解决这些问题,通过调查(1)如何有效区分不同推理水平的中学生的教学; (2)如何相互支持地培养中学生的代数推理和有理数知识。该项目的教育目标是提高未来和实践教师教授认知多样化学生的能力,提高博士生对学生学习与教师实践之间关系的理解,并形成一个致力于持续专业学习如何区分教学的数学教师社区。正在开发三种基于研究的产品:两种学习轨迹、与教师合作开发的区分教学材料以及评估书面评估 学生的推理水平。第一条轨迹为三个推理水平的学生详细阐述,重点是发展代数表达式和求解涉及有理数的基本方程;第二个学习轨迹也为三个推理级别的学生详细阐述,重点关注线性上下文中的共变推理。此外,该项目还调查了差异化教学如何影响学生的课堂体验,这将有助于与跟踪课堂中学生体验的研究结果进行比较。最重要的是,该项目提高了中学数学教师为认知多样化的学生服务的能力。该项目的这一方面有可能缩小机会差距。最后,该项目形成了对帮助未来教师和实践教师学习区分教学所需的各种支持的理解。该项目通过以下方式促进发现和理解,同时促进教学、培训和学习:(a) 将研究融入中学数学教学中,(b) 通过根据学生的认知需求定制教学来促进所有学生的学习,(c) 与实践教师合作学习如何实施这种教学,(d) 改进 培训未来的数学教师和数学教育研究生,以及 (e) 建立一个数学教师社区,他们参与持续学习以实现差异化教学。该项目通过纳入来自代表性不足群体的学生,特别是有学习障碍的学生来扩大参与范围。该项目的成果将通过会议演讲广泛传播;不同媒体发表的文章;一个项目网站,该网站将提供项目产品,成为新闻界和公众获取项目信息的场所,并成为促进教师之间沟通的工具。
项目成果
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